Scaling Functions for Baby Universes in Two-Dimensional Quantum Gravity

TL;DR

This paper investigates the behavior of baby universes in two-dimensional quantum gravity coupled with minimal models, revealing both classical and quantum effects through a transfer matrix approach.

Contribution

It introduces a transfer matrix formalism to analyze baby universe propagation and emission in 2D quantum gravity with minimal models, highlighting quantum effects at finite scales.

Findings

Distribution function for baby universe sizes derived

Classical peak observed in the large k limit

Quantum effects prominent at finite length scales

Abstract

We apply the recently proposed transfer matrix formalism to 2-dimensional quantum gravity coupled to $(2, 2k-1)$ minimal models. We find that the propagation of a parent universe in geodesic (Euclidean) time is accompanied by continual emission of baby universes and derive a distribution function describing their sizes. The $k\to \infty~ (c\to -\infty)$ limit is generally thought to correspond to classical geometry, and we indeed find a classical peak in the universe distribution function. However, we also observe dramatic quantum effects associated with baby universes at finite length scales.